Aspects and embodiment are most generally in the field of rotational motion sensing; more particularly, aspects and embodiments are directed to optical rotational motion sensors, optical rotational motion sensing methods, and applications thereof; most particularly to chip-scale (microscale), integrated, parity-time symmetric laser gyroscope systems, associated methods, and applications.
In 1913, Sagnac demonstrated how the rate of rotation associated with an inertial frame of reference can be determined by optical means. In his experiments, the rotation speed was measured through the phase difference between two beams traveling in opposite directions within a loop. Since then, this approach has been used to develop various families of optical gyroscopes. One breakthrough in this area came shortly after the discovery of the laser, when Macek and Davis introduced gain inside the loop. In this respect, the phase shift between the two counter-propagating beams is effectively converted into a splitting in the resonant frequencies that can in turn be readily measured. In an ideal non-rotating ring laser, the two counter-propagating modes are expected to exhibit the same frequency. On the other hand, if this same system rotates at an angular frequency, the two initially degenerate resonant frequencies split, as given by the following expression
                    Δω        =                                            8              ⁢              π              ⁢                                                          ⁢              A              ⁢                                                          ⁢              Ω                                      L              ⁢                                                          ⁢              λ                                .                                    (        1        )            
Here, λ is the wavelength inside the material, A is the enclosed area, and L is the perimeter of the ring. Ideally, as long as the frequency separation (Δω) exceeds the quantum limit imposed by the spontaneous emission noise, the rotation speed can be uniquely determined through a heterodyne measurement. For example, for a ring laser with a radius of 10 cm operating at a wavelength of 1.55 μm, and rotating at the rate of ˜1°/hour, one can expect a frequency splitting that is at best on the order of ˜0.6 Hz.
In many applications, it is imperative to detect considerably lower angular velocities, i.e., Ω˜10−4°/hour, a precision that is already attained in free-space laser ring gyroscopes. Unfortunately however, such sensitivity levels have so far remained practically out-of-reach in integrated settings where the size of the ring is generally smaller. In addition, due to scattering off the walls of waveguides, the so-called ‘lock-in effect,’ arising from unwanted coupling between the two counter-propagating modes is more pronounced in such on-chip platforms. Finally, most semiconductor gain systems suffer from a higher quantum noise level due to carrier induced index fluctuations.
Semiconductor gain systems have also been considered for implementing ring laser gyroscopes. The main advantage of semiconductors is that they can be electrically pumped directly, therefore they circumvent the requirement for integration of additional pump sources. So far, the best detection rate reported by a single ring is on the order of ˜100 revolution/sec (˜10−8°/hour), although it has been theoretically predicted that centimeter scale InP ring laser gyroscopes can reach rates on the order of 180°/hour. Using a dual-cavity ring laser gyroscope is expected to improve this rate. Ultimately, however, the minimum detectable rotation rate is set by the size of the active ring, which is not easily scalable because of the large non-uniformities across most III-V wafers. In addition, most semiconductor gain systems suffer from higher quantum noise levels due to carrier induced index fluctuations. Considering all the above issues, one may conclude that, without a significant enhancement of intrinsic sensitivity, the prospect of using standard III-V semiconductor microring lasers for detecting rotation rates on the order of ω˜1-100°/hour is daunting.
Measuring rotation rate is of utmost importance in a number of existing and emerging areas of science and technology, from general relativity to robotics, medical-imaging, virtual reality, computer games, unmanned aerial vehicles (drones), and driverless cars. Over the years, various physical phenomena have been utilized to measure the rotation of a frame of reference. Such effects include mechanical movement, Coriolis force, Larmor precession frequency of nuclear spins, and quantum whistling, to name a few. In the realm of optics, the Sagnac effect has been employed to develop some of the finest and most accurate tools for determining rotation rate. Along these lines, free-space ring laser gyroscopes (RLG) and passive fiber optic gyroscopes (FOG) are among the most sensitive rotational sensors built to date. These devices are routinely used for navigation of aircrafts and in defense-related applications.
In recent years, navigation and automation are increasingly becoming indispensable parts of consumer electronics—an area that clearly favors integrated settings and batch fabrication. Despite their superior performance in terms of sensitivity and their resilience to mechanical vibrations, current optical gyroscopes are not as amenable to miniaturization as, for example, their MEMS counterparts are. This is mainly because the Sagnac phase shift that is the physical effect behind the operation of optical gyroscope sis fundamentally proportional to the area enclosed by the optical path that light is traveling around. In order to accumulate sufficient phase in response to small rotations, the area must be large. This raises a question as to whether there is a place for on-chip optical rotational sensors in the growing market of civilian navigation, automation, and even gaming.
The inventors have recognized the benefits and advantages to be realized by a laser ring gyroscope based on the physics of non-Hermitian degeneracies in order to address the issues outlined above. By exploiting the properties of exceptional points in judiciously designed parity-time-symmetric arrangements, the frequency splitting can become proportional to the square-root of the gyration speed, Ω1/2, an effect that can boost the sensitivity to small rotations by orders of magnitude. Moreover, at its maximum sensitivity limit, the splitting no longer depends on the radius of the rings involved. In addition, the lock-in effect can be entirely avoided by enforcing directional propagation in each ring. The embodied invention can open new directions towards the realization of highly sensitive, miniature laser ring gyroscopes on-chip.